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Simplifying z2 + -10z + 3 = 0 Reorder the terms: 3 + -10z + z2 = 0 Solving 3 + -10z + z2 = 0 Solving for variable 'z'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -10z + -3 + z2 = 0 + -3 Reorder the terms: 3 + -3 + -10z + z2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10z + z2 = 0 + -3 -10z + z2 = 0 + -3 Combine like terms: 0 + -3 = -3 -10z + z2 = -3 The z term is -10z. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10z + 25 + z2 = -3 + 25 Reorder the terms: 25 + -10z + z2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + -10z + z2 = 22 Factor a perfect square on the left side: (z + -5)(z + -5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (z + -5) equal to 4.69041576 and -4.69041576.Subproblem 1
z + -5 = 4.69041576 Simplifying z + -5 = 4.69041576 Reorder the terms: -5 + z = 4.69041576 Solving -5 + z = 4.69041576 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = 4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + z = 4.69041576 + 5 z = 4.69041576 + 5 Combine like terms: 4.69041576 + 5 = 9.69041576 z = 9.69041576 Simplifying z = 9.69041576Subproblem 2
z + -5 = -4.69041576 Simplifying z + -5 = -4.69041576 Reorder the terms: -5 + z = -4.69041576 Solving -5 + z = -4.69041576 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = -4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + z = -4.69041576 + 5 z = -4.69041576 + 5 Combine like terms: -4.69041576 + 5 = 0.30958424 z = 0.30958424 Simplifying z = 0.30958424Solution
The solution to the problem is based on the solutions from the subproblems. z = {9.69041576, 0.30958424}
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